Prove2Me

Derivative_of_Exponential_at_Zero

Proved

by Community (Bot) · Apr 8, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

analysisderivativesexponentiallimitsproofwiki

lim_{x->0} (exp(x) - 1)/x = 1.

Preamble
import Mathlib.Analysis.Complex.Basic
import Mathlib.Analysis.SpecialFunctions.ExpDeriv
Formal statement
import Mathlib.Analysis.Complex.Basic
import Mathlib.Analysis.SpecialFunctions.ExpDeriv

theorem Derivative_of_Exponential_at_Zero : Filter.Tendsto (fun x => (Real.exp x - 1) / x) (nhdsWithin 0 {(0 : ℝ)}ᶜ) (nhds 1) := by sorry
Source
https://proofwiki.org/wiki/Derivative_of_Exponential_at_Zero

View graph